Depending on how you cook it, you're going to get different forms of each of those at different rates. On a stove, you can avoid too much moisture and fat from leaving your food by cooking it extremely quickly (in a stir-fry). . You can't sear something in an oven and you can't roast something on the stove. The two are simply not the same, because fundamentally the two are not the same, you are not going to get the same results. It's really as simple as that. You can't take two entirely methods and argue that you get the same results.

Send most of the heat to the surface of the food (good for searing, bad for thorough cooking);

Can be adjusted very quickly, unless they're glass-top;

Can cook food very quickly, because conduction is a very efficient method of heat transfer.

Conventional ovens:

Cook primarily by radiation, unless steaming or simmering in a covered vessel;

Penetrate the food much more readily (good for even cooking);

Take a relatively long time to adjust the temperature;

Tend to have much longer cooking times because the heat disperses so much.

So in general: Use the oven if you need slow, even cooking, or want to dry the food out. Use the stovetop for searing, quick cooking, or if you need precise control over the heat (i.e. caramelizing sugar, stir-frying, etc.).

Thanks for the informative post. My opinions on the oven may have been influenced a lot more by the amount of food I prepare for each meal. As you said, for large amounts of food, the oven often works wonders. I still would like to see some more direct comparisons, but I think I will mark your answer as correct.
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Naomi CampbellDec 10 '10 at 18:35

@Naomi: You can cook large meals on the stove top - you just need a large pot! Ever seen one of those 100-quart stock pots?
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Aaronut♦Dec 10 '10 at 18:55

I have tried it, but I prefer a large shallow baking pan. This way, the contents of the pan are spread out more and can cook faster. The pot usually has to fit within the confines of a 1 foot diameter grill, while the large shallow pan can be heated quickly in an oven.
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Naomi CampbellDec 10 '10 at 19:05

Well, yeah, you usually do the 100-quart stock pot over a bonfire or something. But as long as everything actually fits in one layer on the pan (which it always should - bad idea crowding a skillet or sauce pan) then it'll cook faster than in the oven.
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Aaronut♦Dec 10 '10 at 19:21

Because it's in view and not hidden away in an oven (blocking sight/sound/smell), you can more easily monitor it, and occassionally stir, etc. Because of this, you can more safely put things under higher heat, as you're not just letting it sit, but can move things around so the stuff on the outside doesn't burn.

I've actually considered these points, and I feel as if in most cases the oven outperforms the stove in these areas. In both cases, the contents of the pan will be obscuring the view of the bottom and sides of the pan. In order to know if anything is burning, the pan would have to be checked with a utensil and most likely stirred. Also, from the experimentation I have done, the more even heat spread of the oven provides the ability to cook with less heat and get a more even and faster cooking time. I'm not sure if this is what others have experienced.
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Naomi CampbellDec 10 '10 at 16:26

@Naomi : an even faster cook than a saute or stir-fry?
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JoeDec 10 '10 at 17:02

From the research I have done, the operating temperature of my home stove can be around 500 degrees. When I make my oven stir-fry, the vegetables get crunchy quickly because the top and the bottom are cooking. I first heat the oven to 450 degrees. I usually load up the pan with the sauce (which I also prepare in a sauce pan in the oven), meat, and vegetables, and flip on the broiler. I usually give it one quick stir halfway through and it comes out great. I would need more solid evidence to say one method is faster than the other, but thanks for the great ideas Joe.
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Naomi CampbellDec 10 '10 at 17:58

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@Naomi: The oven will never give you a faster cooking time. A stir-fry can be done in 5 minutes on the stove; even if you use the broiler in the oven, you have to preheat it, so there's about 10 minutes gone before you've even started. Your vegetables are probably getting crunchy quickly because you're drying them out, evaporating all the water in them; that's what ovens do. Cool if that's what you like, but most stir fries have the stated aim of getting tender vegetables.
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Aaronut♦Dec 10 '10 at 18:25

I agree completely with @Aaronut. If you're getting the same results between the two methods and same cooking times... I would suggest you are not stir-frying (on the stove) correctly.
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talon8Dec 10 '10 at 19:15